Power expansions for the self-similar solutions of the modified Sawada-Kotera equation

The fourth-order ordinary differential equation that defines the self-similar solutions of the Kaup—Kupershmidt and Sawada—Kotera equations is studied. This equation belongs to the class of fourth-order analogues of the Painlevé equations. All the power and non-power asymptotic forms and expansions near points z = 0, z = ∞ and near an arbitrary point z = z ₀ are found by means of power geometry methods. The exponential additions to the solutions of the studied equation are also determined.      

解初值问题y″=g(x，y)的含参数块方法

1引言对于二阶常微分方程的初值问题y″=g(x,y),y(x_0)=y_0,y′(x_0)=y_0′,x_0(?)x(?)T(1)的数值解法的研究引起人们的广泛兴趣．对于直接积分(1),自从1976年J．D．Lambert和I．A．Waston提出二阶P-稳定方法和1978年G．Dahlquist证明P-稳定常系数线性多步方法的最高相容阶不超过2的重要结论以来,截止目前,已积累了许多高于2阶的P-稳定方法．例如,修正的Numerov方法,混合法(特殊形式RK的方法),多导法,Obrechkoff方法,显式RKN方法,单隐方法和对角隐式RKN方法等(顺便指出,文献[5,16]中所说的高阶方法的相容阶均不超过4)．所有这些方法,有些相     

Nonstationary wave turbulence

Summary Nonstationary regimes of the wave turbulence evolution are considered in the framework of isotropic kinetic equation. It is predicted analytically and confirmed by numerical experiment that there is a class of wave systems in which any initial distribution of the turbulence energy ink-space comes into a universal, Kolmogorovtype spectrum in a finite time. Before and after the formation of the Kolmogorov spectrum, two different self-similar regimes of evolution occur: the first one is responsible for explosively forming the universal spectrum and the second one determines energy dissipation.     

ELECTRON GUN FOR LARGE ORBIT GYROTRON (LOG) WITH DECREASED INFLUENCE OF CATHODE PLASMA ON ELECTRON BEAM PROPERTIES

High power Large Orbit Gyrotron (LOG) [1] is now under development at FIR FU. First version of this device was recently manufactured and then assembled with power supply ETIGO-IV [2]. Results of preliminary tests of electron-optic system are presented. The conditions when stableflat form of current pulse realized are discussed. Analytical estimations of cathode-anode distance to achieve small influence of cathode plasma during high voltage (HV) pulse are performed. Two new electron gun versions with decreased influence of the cathode plasma on its impedance and pulse form are suggested and optimized. New optimal magnetic field distributions are found. First gun has quiasi-flat cathode configuration near the anode diaphragm and provides operating current about 60 A. Second one uses blade cathode with operating current about 30 A. Beam quality for both guns is suitable for LOG operation.     

A procedure for measuring the flexibility of single wood-pulp fibres

A way of determining the flexibility of wood-pulp fibres is developed, which involves i) a precise measurement of the topology of single-fibres by using a confocal laser scanning microscope and ii) the measurement of the elastic modulus of the fibres by using a single-fibre fatigue cell. Reported in this paper are the initial results of tests carried out on black spruce fibres, which have been subjected to three different levels of mechanical refining energy, namely ∼1100, 2300, and 3500 kWh/t. It is found that the fibre flexibility rises significantly between the first and second energy levels, but it does not change to the same degree between the second and third ones. The described procedure of measuring the flexibility of fibres may be used to establish the appropriate refiner energy necessary for the production of a specific grade of paper. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 115–128, January–February, 2006.     

Second-order necessary optimality conditions for domain optimization problems of the Neumann type

In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987.     

The upper and lower second order directional derivatives of a sup-type function

The purpose of this paper is to give a formula for expressing the second order directional derivatives of the sup-type functionS(x) = sup{f(x, t); t T} in terms of the first and second derivatives off(x, t), whereT is a compact set in a metric space and we assume thatf, f/x and ² f/x ² are continuous on ⁿ × T. We will give a geometrical meaning of the formula. We will moreover give a sufficient condition forS(x) to be directionally twice differentiable.     

One-dimensional harmonic lattice caricature of hydrodynamics: Second approximation

The long-time behavior of an infinite chain of coupled harmonic oscillators is studied. In addition to a limiting hydrodynamic (Euler-type) equation, the next approximation is investigated. The corresponding equation is derived.     

超高真空中银表面垂直谐波电流的实验测量

在超高真空的条件下,测量了清洁、自由银表面产生的光学二次谐波随基波电矢量与入射面之间夹角(?)的变化,从而通过理论公式,求得由Rudnick和Stern引入的,用于衡量垂直面电流密度的唯象参数a的值,在入射基频光波长为1.064μm时,被测定为-4.0±0.8.     

Zur Theorie der Chiralitätsfunktionen

The Algebraic Theory of Chirality Functions is derived by means of exclusively qualitative considerations. Hence, the significance of quantitative results is questionable. Moreover the construction of “Näherungsansätze” (”Approximation-Ansatz”), which may be interpreted as semiempirical methods, is achieved on the basis of plausibility and mathematical simplicity. Since physical arguments are not included, the consistency or inconsistency of “Näherungsansätze” with experimental results do not justify direct physical conclusions.